Correct Answer - Option 1 : 80
Two trains X and Y travelling in the same direction cross each other in 120 seconds. The speed of train Y is 50% of the speed of train X. If speed of train Y increases by 10 m/s, it would take 60 seconds to cross a platform of length 300m. Train X would cross the platform of length 300 m in 30 seconds.
If the lengths of two trains are a and b,
Time taken to cross each other when travelling in same direction = (a + b)/(va - vb)
Time taken to cross each other when travelling in opposite direction = (a + b)/(va + vb)
where va and vb are the speeds of trains A and B respectively.
Let the lengths of X and y be lx and ly respectively.
Let the speeds of X and Y be 2v and v respectively.
(lx + ly)/v = 120
⇒ (ly + 300)/(v + 10) = 60
⇒ (lx + 300)/(2v) = 30
Solving, we get,
⇒ lx = 2100,
⇒ ly = 2700
⇒ v = 40
Speed of train X = 2v = 80 m/s